Download Introduction to Principal Components Analysis

Strategies for Metabolomic
Data Analysis
Dmitry Grapov, PhD
Goals?
Metabolomics
Analytical Dimensions
variables
Samples
Analyzing Metabolomic Data
•Pre-analysis
•Data properties
•Statistical approaches
•Multivariate approaches
•Systems approaches
Pre-analysis
Data quality metrics
• precision
• accuracy
Remedies
• normalization
• outliers
detection
• missing values
imputation
Normalization
• sample-wise
• sum, adjusted
• measurement-wise
• transformation (normality)
• encoding (trigonometric,
etc.)
standard deviation
mean
Outliers
• single
measurements
(univariate)
• two
compounds
(bivariate)
Outliers
univariate/bivariate
\
vs.
multivariate
outliers?
mixed up samples
Transformation
• logarithm
(shifted)
• power
(BOX-COX)
• inverse
Quantile-quantile (Q-Q)
plots are useful for visual
overview of variable
normality
X
X -0.5
Missing Values Imputation
Why is it missing?
•random
•systematic
•
analytical
•
biological
mean
Imputation methods
•single value (mean, min, etc.)
•multiple
•multivariate
PCA
Goals for Data Analysis
Exploration
Classification
• Are there any trends in my data?
– analytical sources
– meta data/covariates
• Useful Methods
– matrix decomposition (PCA, ICA, NMF)
– cluster analysis
• Differences/similarities between groups?
– discrimination, classification, significant changes
• Useful Methods
– analysis of variance (ANOVA)
– partial least squares discriminant analysis (PLS-DA)
– Others: random forest, CART, SVM, ANN
• What is related or predictive of my variable(s) of interest?
– regression
• Useful Methods
– correlation
Prediction
Data Structure
•univariate: a single variable (1-D)
•bivariate: two variables (2-D)
•multivariate: 2 > variables (m-D)
•Data Types
•continuous
•discreet
• binary
Data Complexity
Meta
Data
m
n
variables
Experimental
Design =
complexity
samples
Data
m-D
1-D 2-D
Variable # = dimensionality
Univariate Analyses
univariate properties
•length
•center (mean, median,
geometric mean)
•dispersion (variance,
standard deviation)
•Range (min / max)
standard deviation
mean
Univariate Analyses
•sensitive to distribution shape
•parametric = assumes normality
•error in Y, not in X (Y = mX + error)
•optimal for long data
wide
•assumed independence
•false discovery rate
long
n-of-one
False Discovery Rate (FDR)
univariate approaches do not scale well
• Type I Error: False Positives
•Type II Error: False Negatives
•Type I risk =
•1-(1-p.value)m
m = number of variables tested
FDR correction
Example:
Design: 30 sample, 300 variables
Test: t-test
FDR method: Benjamini and
Hochberg (fdr) correction at q=0.05
Results
FDR adjusted p-values (fdr) or estimate of FDR (Fdr, q-value)
Bioinformatics (2008) 24 (12):1461-1462
Achieving “significance” is a function of:
significance level (α) and power (1-β )
effect size (standardized difference in means)
sample size (n)
Bivariate Data
relationship between two variables
•correlation (strength)
•regression (predictive)
regression
correlation
Correlation
•Parametric (Pearson) or rank-order (Spearman, Kendall)
•correlation is covariance scaled between -1 and 1
Correlation vs. Regression
Regression describes the
least squares or best-fitline for the relationship (Y
= m*X + b)
Bivariate Example
Goal: Don’t miss eruption!
Data
•time between eruptions
– 70 ± 14 min
•duration of eruption
Old Faithful, Yellowstone, WY
– 3.5 ± 1 min
Azzalini, A. and Bowman, A. W. (1990). A look at some data on the Old Faithful
geyser. Applied Statistics 39, 357–365
Bivariate Example
Two cluster pattern for
both duration and
frequency
Azzalini, A. and Bowman, A. W. (1990). A look at some data on the Old Faithful geyser. Applied Statistics 39, 357–365
Bivariate Example
Noted deviations from
two cluster pattern
–Outliers?
–Covariates?
Covariates
Trends in data
which mask
primary goals
can be
accounted for
using covariate
adjustment
and
appropriate
modeling
strategies
Bivariate Example
Noted deviations from
two cluster pattern
can be explained by
covariate:
Hydrofraking 
Covariate adjustment
is an integral aspect of
statistical analyses
(e.g. ANCOVA)
Summary
Data exploration and pre-analysis:
• increase robustness of results
• guards against spurious findings
• Can greatly improve primary analyses
Univariate Statistics:
• are useful for identification of statically
significant changes or relationships
• sub-optimal for wide data
• best when combined with advanced
multivariate techniques
Resources
Web-based data analysis platforms
• MetaboAnalyst(
• MeltDB(
)
http://www.metaboanalyst.ca/MetaboAnalyst/faces/Home.jsp
https://meltdb.cebitec.uni-bielefeld.de/cgi-bin/login.cgi
Programming tools
• The R Project for Statistical
Computing(
)
• Bioconductor(
)
GUI tools
• imDEV(
)
http://www.r-project.org/
http://www.bioconductor.org/
http://sourceforge.net/projects/imdev/?source=directory
)